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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | %feature("docstring") OT::OrthogonalDirection
"Sampling following the orthogonal direction strategy.
Available constructor:
OrthogonalDirection()
OrthogonalDirection(*dimension, k*)
Parameters
----------
dimension : integer
The dimension of the standard space. By default, :math:`dimension = 0` but
automatically updated by the calling class.
k : int
The number of elements in the linear combinations. By default,
:math:`k = 1` but automatically updated by the calling class.
See also
--------
RandomDirection
Notes
-----
This strategy is parameterized by :math:`k \\\\in \\\\{1, \\\\ldots, n\\\\}`, where *n* is
the dimension of the input random vector :math:`\\\\vect{X}`. We generate one
direct orthonormalized basis :math:`(e_1, \\\\ldots, e_n)` uniformly distributed in
the set of direct orthonormal bases. We consider all the normalized linear
combinations of *k* vectors chosen within the *n* vectors of the basis, where
the coefficients of the linear combinations are in :math:`\\\\{+1, -1\\\\}`. This
generates :math:`\\\\binom{k}{n} 2^k` new vectors :math:`v_i`. We sample according
to all the directions defined by the vectors :math:`v_i`.
If :math:`k = 1`, we consider all the axes of the standard space."
// ---------------------------------------------------------------------
%feature("docstring") OT::OrthogonalDirection::generate
"Generate the sample.
Returns
-------
sample : :class:`~openturns.NumericalSample`
The sample generated according to the orthogonal direction strategy."
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